Probability Theory and Related Fields

最新文章

• EXCURSION THEORY FOR ROTATION INVARIANT MARKOV-PROCESSES AI翻译
  作者：VUOLLEAPIALA, J
  摘要：Let (X(t), P(x)) be a rotation invariant (RI) strong Markov process on R(d)\{0} having a skew product representation [\X(t)\, theta(At)], where (theta(t)) is a time homogeneous, RI strong Markov process on S(d-1), \X(t)\ and theta(t) are independent under P(x) and A(t) is a continuous additive functional of \X(t)\. We characterize the rotation invariant extensions of (X(t), P(x)) to R(d). Two examples are given: the diffusion case, where especially the Walsh's Brownian motion (Brownian hedgeho...
• BRANCHING RANDOM-WALK IN RANDOM ENVIRONMENT - PHASE-TRANSITIONS FOR LOCAL AND GLOBAL GROWTH-RATES AI翻译
  作者：GREVEN, A; DENHOLLANDER, F
  作者单位：Utrecht University
  摘要：Let (eta(n)) be the infinite particle system on Z whose evolution is as follows. At each unit of time each particle independently is replaced by a new generation. The size of a new generation descending from a particle at site x has distribution F(x) and each of its members independently jumps to site x +/- 1 with probability (1 +/- h)/2, h is-an-element-of [0, 1]. The sequence {F(x)} is i.i.d. with uniformly bounded second moment and is kept fixed during the evolution. The initial configurati...
• A NEW IDEAL METRIC WITH APPLICATIONS TO MULTIVARIATE STABLE LIMIT-THEOREMS AI翻译
  作者：RACHEV, ST; RUSCHENDORF, L
  作者单位：University of Munster
  摘要：A new ideal metric of order r > 1 is introduced on R(k) and a thorough analysis of its metric properties is given. In comparison to the known ideal metric of Zolotarev this new metric allows estimates from above by pseudo difference moments and thus allows applications to stable limit theorems. As applications we give the right order Berry-Esseen type result in the stable case, obtain the limiting behaviour of multivariate summability methods and discuss the approximation problem by compound P...
• SOME ASYMPTOTICS FOR MULTIMODALITY TESTS BASED ON KERNEL DENSITY ESTIMATES AI翻译
  作者：MAMMEN, E; MARRON, JS; FISHER, NI
  作者单位：Commonwealth Scientific & Industrial Research Organisation (CSIRO); University of North Carolina; University of North Carolina Chapel Hill
  摘要：A test due to B.W. Silverman for modality of a probability density is based on counting modes of a kernel density estimator, and the idea of critical smoothing. An asymptotic formula is given for the expected number of modes. This, together with other methods, establishes the rate of convergence of the critically smoothed bandwidth. These ideas are extended to provide insight concerning the behaviour of the test based on bootstrap critical values.
• MEASURE-VALUED BRANCHING DIFFUSIONS WITH SPATIAL INTERACTIONS AI翻译
  作者：PERKINS, E
  摘要：A strong equation driven by a historical Brownian motion is used to construct and characterize measure-valued branching diffusions in which the spatial motions obey an Ito equation with drift and diffusion depending on the position of an individual and the entire population.
• UNIQUENESS OF THE INFINITE COMPONENT IN A RANDOM GRAPH WITH APPLICATIONS TO PERCOLATION AND SPIN-GLASSES AI翻译
  作者：GANDOLFI, A; KEANE, MS; NEWMAN, CM
  作者单位：New York University; Delft University of Technology
  摘要：We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on Z(d) or Z(d) x N with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on Z(d) or on a slab Z(d) x {0,..., K} and prove both that percolation occurs and that the infinite component is unique for V = Z2 x {0,1} or larger.
• A CHARACTERIZATION OF H-BROWNIAN MOTION BY ITS EXIT DISTRIBUTIONS AI翻译
  作者：VONDRACEK, Z
  摘要：Let X(h) be an h-Brownian motion in the unit ball D subset-of R(d) with h harmonic, such that the representing measure of h is not singular with respect to the surface measure on partial derivative D. If Y is a continuous strong Markov process in D with the same killing distributions as X(h), then Y is a time change of X(h). Similar results hold in simply connected domains in C provided with either the Martin or the Euclidean boundary.
• THE SUBMARTINGALE PROBLEM FOR BROWNIAN-MOTION IN A CONE WITH NONCONSTANT OBLIQUE REFLECTION AI翻译
  作者：KWON, Y
  摘要：This work is concerned with the existence and uniqueness of a strong Markov process that has continuous sample paths and the following additional properties. 1. The state space is a cone in d-dimensions (d greater-than-or-equal-to 3), and the process behaves in the interior of the cone like ordinary Brownian motion. 2. The process reflects instantaneously at the boundary of the cone, the direction of reflection is continuous except at the vertex and has a limit which is fixed on each radial li...
• MAJORIZATION OF GAUSSIAN-PROCESSES AND GEOMETRIC APPLICATIONS AI翻译
  作者：GORDON, Y
  摘要：Let (x(i)*)i = 1n denote the decreasing rearrangement of a sequence of real numbers (x(i))i = 1n. Then for every i not-equal j, and every 1 less-than-or-equal-to k less-than-or-equal-to n, the 2-nd order partial distributional derivatives satisfy the inequality, partial derivative 2/partial derivative x(i) partial derivative x(j) [GRAPHICS] less-than-or-equal-to 0. As a consequence we generalize the theorem due to Fernique and Sudakov. A generalization of Slepian's lemma is also a consequence ...
• LARGE DEVIATIONS FOR THE INVARIANT MEASURE OF A REACTION-DIFFUSION EQUATION WITH NON-GAUSSIAN PERTURBATIONS AI翻译
  作者：SOWERS, R
  作者单位：University of Southern California
  摘要：In this paper we establish a large deviations principle for the invariant measure of the non-Gaussian stochastic partial differential equation (SPDE) partial derivative t-upsilon(epsilon) = L-upsilon(epsilon) + f(x, upsilon(epsilon)) + epsilon-sigma(x, upsilon(epsilon)) W(tx). Here L is a strongly-elliptic second-order operator with constant coefficients, Lh:= DH(xx) - alpha-h, and the space variable x takes values on the unit circle S1. The functions f and sigma are of sufficient regularity t...